Natick MA - William GREENE m Mary E. Moran 1894

Seeking info regarding the GREENE Family of Natick, MA.Wm.B.,b. 1865,d. 1945,son of William Greene and Catherine GARVEY, m. Mary E. MORAN 5/15/1894. Had daughter Helen Mae who married Geo. BEAL. She was my grandmother.
The family lived off of Main St. in Natick. William and Catherine both born in Ireland according to 1920 census. I am STUCK as to history of William and Catherine. ANY help would be appreciated. Thank you.